The choice of sample size for mortality forecasting: A Bayesian learning approach

Forecasted mortality rates using mortality models proposed in therecent literature are sensitive to the sample size. In this paper we propose a method based on Bayesian learning to determine model-specific posterior distributions of the sample sizes. In particular, the sample size is included as an extra parameter in the parameter space of the mortality model, and its posterior distribution is obtained based on historical performance for different forecast horizons up to 20 years.Age- and gender-specific posterior distributions of sample sizes arecomputed. Our method is applicable to a large class of linear mortality models. As illustration, we focus on the first generation of the Lee-Carter model and the Cairns-Blake-Dowd model. Our methodis applied to U.S. and Dutch data. For both countries we find highlyconcentrated posterior distributions of the sample size that are gender- and age-specific. In the out-of-sample forecast analysis, the Bayesian model outperforms the original mortality models with fixed sample sizes in the majority of cases.